Physics 114C - Mechanics Lecture 16 (Walker: Ch. 7.1-2) Work & Energy February 3, 2012 John G....

Physics 114C - MechanicsLecture 16 (Walker: Ch. 7.1-

2)Work & EnergyFebruary 3, 2012

Physics 114C - MechanicsLecture 16 (Walker: Ch. 7.1-

2)Work & EnergyFebruary 3, 2012

John G. CramerProfessor Emeritus, Department of Physics

B451 [email protected]

AnnouncementsAnnouncements Because the last two problems of HW#4 are covered in

today’s lecture, I moved the due date for HW#4 to 11:59 PM on Friday, February 3 (tonight). HW#5 is still due at 11:59 PM on Thursday, February 9. HW#6 is due at 11:59 PM on Thursday, February 16.

Register your clicker.

We will have Exam 2 on Friday, February 10. It will cover Chapters 5-8 and will be similar to Exam 1 in its structure. There will again be assigned seating. If you have not already done so and would like to request a left-handed seat, right-handed aisle seat, or front row seat, E-mail your request to me ASAP.

February 3, 2012 2/28Physics 114A - Lecture 16

Physics 114A - Introduction to Mechanics - Winter-2012

Lecture: Professor John G. Cramer

Textbook: Physics, Vol. 1 (UW Edition), James S. Walker

Week Date L# Lecture Topic Pages Slides Reading HW Due Lab

423-Jan-12 E1 EXAM 1 - Chapters 1-4

1-D Dynamics24-Jan-12 10 Newton's Laws 14 29 5-1 to 5-4

26-Jan-12 11 Common Forces 11 26 5-5 to 5-7

27-Jan-12 12 Free Body Diagrams - 24 - HW3

530-Jan-12 13 Friction 9 27 6-1

Newton's Laws Tension

31-Jan-12 14 Strings & Springs 12 29 6-2 to 6-4

2-Feb-12 15 Circular Motion 5 30 6-5

3-Feb-12 16 Work & Energy 11 23 7-1 to 7-2 HW4

66-Feb-12 17 Work & Power 7 25 7-3 to 7-4

Work-energy7-Feb-12 18 Potential Energy 10 26 8-1 to 8-2

9-Feb-12 19 Energy Conservation I 16 18 8-3 to 8-5 HW5

10-Feb-12 E2 EXAM 2 - Chapters 5-8

Lecture Schedule (Part 2)

Lecture Schedule (Part 2)

We are here.


Circular Orbits (1)Circular Orbits (1)

Thought Experiment: On an airless planet, cannon balls are shot from a cannon mounted on a tower ar increasing muzzle velocities, and go farther and farther as the velocity is increased. What limits their range?


Circular Orbits (2)Circular Orbits (2)

( , toward center)w mg

( , toward center)w mg

2

( , toward center)

( ), so

net

orbitr orbit

Fa g

m

va g v rg

r

6 2(6.37 10 m)(9.80 m/s ) 7,900 m/s 16,000 mphorbitv rg February 3, 2012 5/28Physics 114A - Lecture 16

A satellite moves at constant speed in a circular orbit about the center of the Earth and near the surface of the Earth. If the magnitude of its acceleration is g = 9.81 m/s2 and the Earth’sradius is 6,370 km, find:(a) its speed v; and(b) the time T required for one completerevolution.

Example: A Satellite’s Motion

Example: A Satellite’s Motion

2

cp

va g

r

3 2 3(6,370 10 m)(9.81 m/s ) 7.91 10 m/s 17,700 mi/hv rg 3 32 / 2 (6,370 10 m) /(7.91 10 m/s) 5,060 s 84.3 minT r v


Note: if you dug a tunnel directly through the center of the Earth anddropped in a subway car, its round-trip transit time would also be 84.3 minutes.

Work Done by a Constant Force


The definition of work, when the force is parallel to the displacement:

(7-1)

SI work unit:newton-meter (N·m) = joule, J


Typical WorkTypical Work


Work for Force at an AngleWork for Force at an AngleIf the force is at an angle to the displacement: (7-3)

Only the horizontal component of the force does any work (horizontal displacement).February 3, 2012 9/28Physics 114A - Lecture 16

Work SummaryWork Summary Energy is transferred from person to spring as the person stretches the spring. This is “work”.

W F x

cosxW F x F x

Work = 0

SI Units for work:

1 joule = 1 J = 1 N·m

1 electron-volt = 1 eV = 1.602 x 10-19 J



Work Done by a Constant Force The work can also be written as the dot

product of the force F and the displacement d:


Negative and Positive WorkNegative and Positive Work

The work done may be positive, zero, or negative, depending on the angle between the force and the displacement:


Perpendicular Force and Work

Perpendicular Force and Work

A car is traveling on a curved highway. The force due to friction fs points toward the center of the circular path.

How much work does the frictional force do on the car?

Zero!

General Result: A force that is everywhere perpendicular to the motion does no work.


Work on a System withMany Forces

Work on a System withMany Forces

total 1 1 2 2 3 3x x xW F x F x F x

Model the system as a particle a single x

total 1 2 3

1 2 3 net ( )x x x

x x x x

W F x F x F x

F F F x F x



Work Done by a Constant Force If there is more than one force acting on

an object, we can find the work done by each force, and also the work done by the net force:

(7-5)


Example: Pulling a Suitcase

Example: Pulling a Suitcase

A rope inclined upward at 45o pulls a suitcase through the airport. The tension on the rope is 20 N.

How much work does the tension do, if the suitcase is pulled 100 m?

( ) cosW T x

(20 N)(100 m)cos 45 1410 JW

Note that the same work could have been done by a tension of just 14.1 N by pulling in the horizontal direction.


Gravitational WorkGravitational Work In lifting an object of weight mg by a height h, the person doing the lifting does an amount of work W = mgh.

If the object is subsequently allowed to fall a distance h, gravity does work W = mgh on the object.

W mgh


Example: Loading with a Crane

Example: Loading with a Crane

A 3,000 kg truck is to be loaded onto a ship by a crane that exerts an upward force of 31 kN on the truck. This force, which is large enough to overcome the gravitational force and keep the truck moving upward, is applied over a distance of 2.0 m.

(a) Find the work done on the truck by the crane.

(b) Find the work done on the truck by gravity.

(c) Find the net work done on the truck.app app (31 kN)(2.0 m) 62 kJyW F y

2g (3000 kg)( 9.81 m/s )(2.0 m) 58.9 kJyW mg y

net app g (62.0 kJ) ( 58.9 kJ) 3.1 kJW W W


Positive & NegativeGravitational WorkPositive & NegativeGravitational Work

When positive work is done on an object, its speed increases; when negative work is done, its speed decreases.


Kinetic Energy &The Work-Energy Theorem


After algebraic manipulations of the equations of motion, we find:

Therefore, we define the kinetic energy:

(7-6)

2 2 2 22 2f i f iv v a x mv mv F x




Work-Energy Theorem: The total work done on an object is equal to its change in kinetic energy.

(7-7)


Clicker Question 1Clicker Question 1

b) 0.707 va) 0.50 v e) 2.00 vd) 1.414 vc) v

Car 1 has twice the mass of Car 2, but they both have the same kinetic energy. If the speed of Car 1 is v, approximately what is the speed of Car 2?


Problem Solving Strategy

Problem Solving Strategy

Picture: The way you choose the +y direction or the +x direction can help you to easily solve a problem that involves work and kinetic energy.

Solve:1. Draw the particle first at its initial position and second at its final position. For convenience, the object can be represented as a dot or box. Label the initial and final positions of the object.2. Put one or more coordinate axes on the drawing.3. Draw arrows for the initial and final velocities, and label them appropriately.4. On the initial-position drawing of the particle, place a labeled vector for each force acting on it.5. Calculate the total work done on the particle by the forces and equate this total to the change in the particle’s kinetic energy.

Check: Make sure you pay attention to negative signs during your calculations. For example, values for work done can be positive or negative, depending on the direction of the displacement relative to the direction of the force. Kinetic energy values, however, are always positive.February 3, 2012 23/28Physics 114A - Lecture 16

Example: A Dogsled RaceExample: A Dogsled Race During your winter break, you enter a “dogsled” race across a frozen lake, in which the sleds are pulled by students instead of dogs. To get started, you pull the sled (mass 80 kg) with a force of 180 N at 40° above the horizontal. The sled moves x = 5.0 m, starting from rest. Assume that there is no friction.

(a) Find the work you do.

(b) Find the final speed of your sled.

total you cos

(180 N)(cos 40 )(5.0 m) 689 J

xW W F x F x

1 1 12 2 2total 2 2 2f i fW mv mv mv

2 total2f

Wv

m

total2 2(689 J)4.15 m/s

(80 kg)f

Wv

m


Example: Work and Kinetic Energy in a Rocket Launch

Example: Work and Kinetic Energy in a Rocket Launch

A 150,000 kg rocket is launched straight up. The rocket engine generates a thrust of 4.0 x 106 N. What is the rocket’s speed at a height of 500 m? (Ignore air resistance and mass loss due to burned fuel.)

6 9thrust thrust ( ) (4.0 10 N)(500 m) 2.0 10 JW F y

4 2 9grav ( ) ( ) (1.5 10 kg)(9.80 m/s )(500 m) 0.74 10 JW w y mg y

1 2 9thrust grav2

0 1.26 10 JK mv W W 2129.6 m/s

Kv

m


Example: Pushing a PuckExample: Pushing a Puck

A 500 g ice hockey puck slides across frictionless ice with an initial speed of 2.0 m/s. A compressed air gun is used to exert a continuous force of 1.0 N on the puck to slow it down as it moves 0.50 m. The air gun is aimed at the front edge of the puck, with the compressed air flow 30o below the horizontal.

What is the puck’s final speed?

( ) cos (1.0 N)(0.5 m)cos150 0.433 JW F r

1 12 21 02 2

K mv mv W

2 21 0

2 2( 0.433 J)(2.0 m/s) 1.51 m/s

(0.5 kg)

Wv v

m


Example: Work on an Electron

Example: Work on an Electron

In a television picture tube, electrons are acceleratedby an electron gun. The force that accelerates theelectron is an electric force due to the electric fieldin the gun. An electron is accelerated from rest by anelectron gun to an energy of 2.5 keV (2,500 eV) over a distanceof 2.5 cm. (1 eV = 1.60 x 10-19 J)

Find the force on the electron, assuming that it is constant and in the direction of the electron’s motion.

19

14

(2,500 ev)(1.6 10 J/eV) 0

(0.025 m)

1.6 10 N

f ix

K KF

x

x f iF x K K totalW K


Before Monday, read Walker Chapter 7.3-4

Homework Assignments #4 should be submitted using the Tycho system by11:59 PM on Friday, February 3 (Tonight!)

Register your clicker, using the “Clicker” link on the Physics 114A Syllabus page.

End of Lecture 16End of Lecture 16


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Physics 114C - Mechanics Lecture 16 (Walker: Ch. 7.1-2) Work & Energy February 3, 2012 John G....

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